Bernoulli's experiences

Maybe you found this blog while searching for texts related to physics, maths and/or one of the scientists named Bernoulli. Though, every now and then, I might write about maths, the main scope concerns the world of chess problems - views, experiences, pleasures, moments of frustration (indeed!). In most cases, posts are about solving, constructing, enjoying chess compositions.

28 September 2012

Let's start with a construction task: create a twomover that shows the return of the piece that makes the key move as often as possible. Provided, no promoted pieces are used and no duals are allowed, the maximum seems to be 29. In 1980, Bernd Schwarzkopf had published a position with mate duals. Without knowing that, I made my own attempts (there was a little contest) about ten years laster and published a correct twomover. You'll surely find all the solutions, right?

Gerson Berlinger

32er Nr. 1-2, 1990

#2
29 solutions

(11+3)

The next diagram is a 16-in-1 problem. Have fun figuring out the solutions.

George Burt Spencer

St. Paul Dispatch, 1906

#2
on each file and rank

(34+15)

Finally, a little retro puzzle.

Nikolai Beluchow

Die Schwalbe 12/2011

By mistake, two chess positions were rotated at a random angle each and then printed onto the same chess diagram. No two pieces were printed one over the other. Separate the two positions and orientate each one correctly! (11+7)

21 September 2012

Already a long time ago I had made plans to write about this special fairy piece. Finally, I am ready to do so.

The imitator can be compared to a shadow. It can't capture nor can it be captured nor give check. Whenever a pieces moves, the imitator moves exactly in the same way. Of course, there are some restrictions.

An imitator can't cross an occupied square except when it imitates a hopper and also has to have a hurdle. A move is illegal if it can't be accompanied by a legal move of an imitator, i.e. putting it on an occupied square (after the piece has moved) or off the board.

Normally, an imitator imitates moves of both sides, but you can also declare it to do so only when either White or Black moves. In general, the symbol is a black circle.

With more than one imitator on the board, a move is only legal, if all of them can imitate it. The promotion to an imitator is legal, but can be excluded.

The following quite simple diagram demonstrates the effect an imitator has.

Legal moves?

a) Black to move:
Rd8 (Id6)
Rc8 (Ic6)
Rb8 (Ib6)
0-0 (Ia6)
Kf8 (Ib6)+
Kf7 (Ib5)+
You can see that the imitator move is written in (round) brackets.
The imitator shields the white king from checks. Therefore, a king move puts White in check.
Moves like Ra7 or Rh5 or Ke7 are not allowed as the white king blocks the imitator.
Castling long is not possible, because the first part is the king move which is not allowed due to the position of the imitator. On the other hand, castling short works, as the imitator goes to c6 after the king move and returns to a6 after the rook move.

b) White to move:
Kb5 (Ib6)
Ka6 (Ia7)
Ka4 (Ia5)
Kb6 (Ib7)
Kb4 (Ib5)
Observe that the white knight can't move at all. It's pinned, for any move would put the white king in check which is not allowed.